
Our plan now is to analyze this exact sequence.
In [1]}, the authors introduced a conjecture which is known in the literature as Conjecture A.
Its original formulation asserts that for an elliptic curve \( E \)  over any number filed \( F \) , the Pontryagin dual of the classical fine Selmer group over the cyclotomic extension \( F_{\mathrm {cyc}}\)  is a finitely generated \( \mathbb {Z}_p \) -module.
Here, we use an equivalent cohomological version of Conjecture A (cf. [2]}).
